Causal graphs represent structural relationships among variables, yet users must still interpret direction, mechanism, and adjustment conditions in relation to the task at hand. Prior work often compares explanation formats as fixed conditions and pays less attention to how users distribute reasoning across graphs, direct explanations, and stories. We developed CoNS-Explorer, which uses reviewed instructional DAGs/SCMs to maintain a shared causal-fact ledger and generate fact-matched direct explanations and contextualized stories. A controlled survey experiment ($N=240$) compared the two texts as complete presentation packages. In the primary GLMM, the Story condition had a positive but uncertain overall association with accuracy (OR $=1.55$, 95\% CI $[0.34,7.10]$, $p=.572$); a population-averaged GEE showed a significant positive effect (OR $=1.89$, 95\% CI $[1.02,3.48]$, $p=.042$). Task-type interactions localized the clearest advantage to total-effect adjustment. Story also significantly increased situational presence. In a separate system-task and interview study ($N=24$), participants freely used graphs, direct explanations, and stories across three causal models. They established structural anchors with graphs and numerical results, consulted text when direction was unclear, mechanisms were unfamiliar, or multiple paths competed, and checked their judgments against other representations or external evidence. Integrating the two studies, we develop a process framework of structural anchoring, uncertainty triggering, explanation routing, and cross-calibration, together with four testable design propositions for adaptive causal explanation.

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